In navigation systems, a heading represents the direction a vehicle is facing or pointing. Ocean-going vessels use heading sensors to monitor the location and the orientation of the vessels as well as objects towed by such vessels. For example, towed array sensors require heading sensors to monitor and control the location and the orientation of the towed array sensors. In some configurations, three sensors are used to measure the gravitational field strength in a full spatial (3-axis) orientation and three other sensors are used to measure the magnetic field strength also in the full spatial (3-axis) orientation. Other approaches include use of compass cards, magnetometers mounted on float assemblies, and capacitive/electrostatic field strength accelerometers. However, these approaches suffer from various deficiencies such as limited accuracy across different latitudes, susceptibility to damage from mechanical shock, and lack of stability and repeatability. Alternatives are desired.